The gain of this initial step lies in the fact that \(K\) -spherical functions can be studied by established methods of group theory. In Section , we shall use the Cartan decomposition of the superconformal group to construct the crossing symmetry equations. Before [1]}, these equations have been constructed only in a limited number of cases. In Section , we turn to superconformal blocks. They will be characterised as eigenfunctions of the Laplace–Beltrami operator within the space of \(K\) -spherical functions. In bosonic theories,Throughout the text we will use the word “bosonic” to refer to theories which do not posses supersymmetry. These theories can have both bosonic and fermionic fields. this eigenvalue problem assumes the form of a matrix-valued Schrödinger equation that generalises the \(BC_2\)  Calogero–Sutherland system. This allows to express the blocks in many cases in terms of known special functions. In the supersymmetric setup, partial waves will be obtained from the bosonic ones through a quantum mechanical perturbation theory that becomes exact at a small finite order.
